2026/2027

Введение в кэлерову геометрию

Статус: Дисциплина общефакультетского пула

Кто читает: Факультет математики

Где читается: Факультет математики

Когда читается: 3, 4 модуль

Охват аудитории: для всех кампусов НИУ ВШЭ

Преподаватели: Голота Алексей Сергеевич

Язык: английский

Кредиты: 6

Контактные часы: 72

Course Syllabus

Abstract

Compact Kaehler manifolds form a class of compact complex manifolds that is remarkable from the complex-analytic, differential-geometric and algebro-geometric viewpoints. This class includes smooth complex projective varieties, as well as many non-algebraic complex manifolds. The main advantage of compact Kaehler manifolds is the existence of the so-called Hodge decomposition on cohomology. Building the theory of compact Kaehler manifolds and proving the existence of Hodge decomposition requires methods from a few important areas of modern mathematics (complex analysis, differential geometry, algebraic geometry, functional analysis and PDEs). This course will be a concise introduction to geometry of compact Kaehler manifolds.